Methods and systems of using result buffers in parity operations

ABSTRACT

A disk controller includes memory that is accessible by both a microprocessor and hardware parity logic. Parity-related operations are identified by scenario, and parity coefficient subsets are stored in a memory table for each different parity-related calculation scenario. To perform a particular parity-related operation, the microprocessor determines the operation&#39;s scenario and identifies the corresponding coefficient subset. The hardware parity logic is then instructed to perform the appropriate parity computation, using the identified coefficient subset. In one embodiment, parity segments are calculated by a parity segment calculation module that is embodied as an application specific integrated circuit (ASIC). The ASIC includes one or more result buffers for holding intermediate computation results, one or more mathematical operator components configured to receive data segments and coefficients associated with the data segments and operate on them to provide intermediate computation results that can be written to the one or more result buffers, and one or more feedback lines. The feedback lines are coupled between an associated result buffer and an associated mathematical operator component and provide an intermediate computation result to the math operator for use in calculating parity segments.

TECHNICAL FIELD

[0001] This invention relates to parity operations in redundant disk drive systems, and particularly to parity operations in such systems that utilize two or more parity segments per storage stripe.

BACKGROUND OF THE INVENTION

[0002] Modem, high-capacity data storage systems often utilize a plurality of physical disk drives for redundant storage of data. This arrangements speeds data access as well as protecting against data loss that might result from the failure of any single disk.

[0003] There are two common methods of storing redundant data. According to the first or “mirror” method, data is duplicated and stored on two separate areas of the storage system. In a disk array, for example, identical data is stored on two separate disks. This method has the advantages of high performance and high data availability. However, the mirror method is also relatively expensive, effectively doubling the cost of storing data.

[0004] In the second or “parity” method, a portion of the storage area is used to store redundant data, but the size of the redundant storage area is less than the remaining storage space used to store the original data. For example, in a disk array having six disks, five disks might be used to store data, with the sixth disk being dedicated to storing redundant data, which is referred to as “parity” data. The parity data allows reconstruction of the data from one data disk, using the parity data in conjunction with the data from surviving disks. The parity method is advantageous because it is less costly than the mirror method, but it also has lower performance and availability characteristics in comparison to the mirror method.

[0005] One aspect of this invention involves storing redundant data according to parity techniques. In conventional disk arrays utilizing parity storage, the space on the storage disks are configured into multiple storage stripes, where each storage stripe extends across the storage disks. Each stripe consists of multiple segments of storage space, where each segment is that portion of the stripe that resides on a single storage disk of the disk array.

[0006]FIG. 1 illustrates a conventional disk array 12 having six storage disks 13. In this simplified example, there are five storage stripes extending across the storage disks. FIG. 1 highlights data and storage segments of a single one of these five stripes. Data segments of the indicated stripe are indicated by cross-hatching. The corresponding parity segment of this same stripe is illustrated in solid black. Generally, of the six segments comprising any given stripe, five of the segments are data segments and the sixth segment is a parity segment.

[0007] This type of parity storage is referred to as 5+1 parity storage, indicating that there are five data segments for every single parity segment. This scheme is more generally referred to as N+1 grouping, where N is the actual number of data segments in a data stripe.

[0008] N+1 redundancy grouping such as illustrated in FIG. 1 protects against the loss of any single physical storage device. If the storage device fails, its data can be reconstructed from the surviving data. The calculations performed to recover the data are straightforward, and are well-known. Generally, a single parity segment P is calculated from data segments D₀ through D_(N−1) in accordance with the following equation:

P=x ₀ +x ₁ +x ₂ +x _(N−1)

[0009] where x₀ through x_(N−1) correspond to the data from data segments D₀ through D_(N−1) After the loss of any single data segment, its data can be recovered through a straightforward variation of the same equation.

[0010] In many systems, however, it is becoming important to protect against the loss of more than a single storage device. Thus, it is becoming necessary to implement N+2 grouping in redundant storage systems.

[0011] While N+2 redundancy grouping enhances data protection, it also involves more complex calculations—both in initially calculating parity segments and in reconstructing any lost data segments.

[0012] A general form of the N+2 parity computation is as follows:

P=p ₀ x ₀ +p ₁ x ₁ +p ₂ x ₂ +p _(N−1) x _(N−1)

Q=q ₀ x ₀ +q ₁ x ₁ +q ₂ x ₂ +q _(N−1) x _(N−1)

[0013] where:

[0014] P is the value of a first parity segment;

[0015] Q is the value of a second parity segment;

[0016] x₀ through x_(N−1) are the values of the data segments

[0017] p₀ through p_(N−1) and q₀ through q_(N−1) are constant coefficients that are particular to a given parity scheme.

[0018] These equations form a two-equation system that, by the rules of linear algebra, can potentially solve for any two unknowns x_(a) through x_(b) which represent the data from a single stripe of any two failed storage devices. One requirement is that the two sets of coefficients p_(i) and q_(i) be linearly independent. This requirement is met, for example, if p₀=1, p₁=1, p₂=1; etc.; and q₀=1, q₁=2, q₂=3; etc. Other examples are also possible.

[0019] The mathematics of N+2 parity are well-known and are not the primary subject of this description. However, it is apparent from the brief description given above that N+2 parity computations are significantly more complex than N+1 parity computations. In actual implementations of N+2 disk arrays, this complexity threatens to limit the data throughput of storage device controllers and, consequently, of the overall disk array.

[0020] This invention includes methods and means for maintaining adequate data throughput in spite of the added complexity resulting from N+2 parity calculations.

SUMMARY

[0021] In accordance with one aspect of the invention, every possible parity-related computation is identified as a different scenario. A coefficient subset is selected or computed for each different scenario and stored in a memory table during an initialization process. To perform a particular operation, its scenario is identified and the corresponding coefficient subset is located. Hardware logic is then instructed to perform the actual parity operation, using the identified coefficient subset. This allows very efficient computations, using coefficients that are computed and selected ahead of time. In one embodiment, parity segments are calculated by a parity segment calculation module that is embodied as an application specific integrated circuit (ASIC). The ASIC includes one or more result buffers for holding intermediate computation results, one or more mathematical operator components configured to receive data segments and coefficients associated with the data segments and operate on them to provide intermediate computation results that can be written to the one or more result buffers, and one or more feedback lines. The feedback lines are coupled between an associated result buffer and an associated mathematical operator component and provide an intermediate computation result to the math operator for use in calculating parity segments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022]FIG. 1 is a block diagram showing N+1 redundancy grouping in accordance with the prior art.

[0023]FIG. 2 is a block diagram showing N+2 redundancy grouping as used in the described embodiment of the invention.

[0024]FIG. 3 is a block diagram illustrating layout of a memory table in accordance with the invention.

[0025]FIG. 4 is a flowchart illustrating preferred steps in accordance with the invention.

[0026]FIG. 5 is a block diagram showing pertinent components of a disk controller in accordance with the invention.

DETAILED DESCRIPTION

[0027] Parity Operations

[0028] Referring to FIG. 2, a redundant data storage system 20 in accordance with the invention utilizes storage disks 22 with data stripes 24. Each data stripe 24 comprises a plurality of data segments x₀ through x_(N−1) and at least two corresponding parity segments P and Q. P and Q are derived from the data segments x₀ through x_(N−1), from a first set of parity coefficients p₀ through p_(N−1), and from a second set of parity coefficients q₀ through q_(N−1). The parity coefficients correspond to respective data segments in accordance with the equations below:

P=p ₀ x ₀ +p ₁ x ₁ +p ₂ x ₂ +p _(N−1) x _(N−1)

Q=q ₀ x ₀ +q ₁ x ₁ +q ₂ x ₂ +q _(N−1) x _(N−1)

[0029] In accordance with the invention, parity operations are generally classified as parity segment generation operations, parity segment regeneration operations, and data segment reconstruction operations.

[0030] A parity segment generation operation is performed when creating a new data stripe—the parity segments are created based on completely new data.

[0031] A parity segment regeneration operation is performed with respect to an existing stripe, either when new data causes the addition of a new data segment or when a read/modify/write cycle modifies one or more data segments. In a parity segment regeneration operation, the parity segments are modified incrementally, without reading an entire data stripe. For example, suppose that new data causes the addition of a new data segment x₄. P_(NEW) is calculated as follows:

P _(NEW) =P _(OLD) +p ₄ x ₄

[0032] Similarly, suppose that data segment x₂ is modified as the result of a read/modify/write cycle. In this case, P_(NEW) is calculated as follows:

P _(NEW) =P _(OLD) p ₂ x _(2OLD) +p ₂ x _(2NEW)

[0033] Calculating new P and Q values from the old data segment values involves significantly fewer memory reads than calculating P and Q from scratch after every stripe modification.

[0034] In accordance with the invention, parity segment regeneration operations are further classified as either parity regenerations resulting from added data segments or parity regenerations resulting from a modified data segment.

[0035] Data segment reconstruction operations include two sub-classifications: single data segment reconstruction operations and double data segment reconstruction operations. A single data segment can be reconstructed from either the P or the Q parity segment in combination with the surviving data segments. Generally, a data segment x_(a) is reconstructed from either parity segment P or Q as follows:

x _(a) =f(p ₀ , p _(a))x ₀ +f(p₁ , p _(a))x ₁ + . . . +f(p_(a))P+ . . . +f(p _(N−1) , p _(a))x _(N−1)

x _(a) =f(q ₀, q_(a))x ₀ +f(q₁ , q _(a))x ₁ + . . . +f(q_(a))Q+ . . . +f(q _(N−1), q_(a))x _(N−1)

[0036] where f( ) is a transformation function that generates an appropriate coefficient particular to the parity generation code being used.

[0037] One implementation of these equations is as follows:

x _(a) =p _(a) ⁻¹(p ₀ x ₀ +p ₁ x ₁ + . . . +P+ . . . +p _(N−1) x _(N−1))

x _(a) =p _(a) ⁻¹(q ₀ x ₀ +q x _(i) + . . . +Q+ . . . +q _(N−1) x _(N−1))

[0038] Two data segments can be reconstructed from the P and the Q parity segments in combination with the surviving data segments. Generally, two data segments x_(a) and x_(b) are reconstructed from parity segments P and Q as follows:

x _(a) =f(p ₀ , q ₀ , p _(a) , p _(b) , q _(a) , q _(b))x ₀ +f(p ₁ , q ₁ , p _(a) , p _(b) , q _(a) , q _(b))x ₁ + . . . f(p _(a) , p _(b) , q _(a) , q _(b))P+f(p _(k) , q _(k) , p _(a) , p _(b) , q _(a) , q _(b))x _(k) +f(p _(k+) , q _(k+1) , p _(a) , p _(b) , q _(a) q _(b))x _(k+1) + . . . f(p _(a) , p _(b) , q _(a) , q _(b))Q+ . . . +f(p _(N−1) , q _(N−1) , p _(a) , p _(b) , q _(a) , q _(b))x _(N−1)

x _(b) =f(p ₀ , q ₀ , p _(a) , p _(b) , q _(a) , q _(b))x ₀ +f(p ₁ , q ₁ , p _(a) , p _(b) , q _(a) , q _(b))x ₁ +f(p _(a) , p _(b) , q _(a) , q _(b))P+f(p _(k) , q _(k) , p _(a) , p _(b) , q _(a) , q _(b))x _(k) +f(p _(k+1) , q _(k+1) , p _(a) , p _(b) , q _(a) , q _(b))x _(k+1) + . . . +f(p _(a) , p _(b) , q _(a) , q _(b))Q+ . . . +f(p _(N−1) , q _(N−1) , p _(a) , p _(b) , q _(a) , q _(b))x _(N−1)

[0039] where f( ), again, is a transformation function that generates an appropriate coefficient particular to the parity generation code being used.

[0040] One implementation of these equations is as follows:

x _(a)=(p, q _(b) +p _(b) q _(a))⁻¹((q _(b) p ₀ +p _(b) q ₀)x ₀+(q ₀ p ₁ +p ₀ q ₁)x ₁ + . . . +q _(b) P+ . . . +(q _(b) p _(k) +p _(b) q _(k))x _(k+)(q _(b) p _(k−1) +p _(b) q _(k+1))x _(k+) + . . . +p _(b) Q+ . . . +(q _(b) p _(N−1) +p _(b) q _(N−1))x _(N−1))

x _(b)=(p _(a) q _(b) +p _(b) q _(a))⁻¹((q _(a) p ₀ +p _(a) q ₀)x ₀+(q _(a) p ₁ +p _(a) q ₁)x ₁ + . . . +q _(a) P+ . . . +(q _(a) p _(k) +p _(a) q _(k))x _(k)+(q _(a) p _(k−1) +p _(a) q _(k+1))x _(k+) + . . . +p _(a) Q+ . . . +(q _(a) p _(N−1) +p _(a) q _(N−1))x _(N−))

[0041] Generally, all of the parity operations described above can be accomplished by using a different combination of known coefficients chosen from a base set having a finite number of such coefficients. These coefficients include p₀-p_(N−1), q₀-q_(N−1), and the coefficients resulting from the transform functions f( ). Any particular parity operation utilizes a subset of these coefficients, depending on the actual data or parity segment being calculated. The particular subset of coefficients needed for a particular calculation depends on both the classification of the operation and upon the specific data and/or parity segments involved. Thus, within a given classification of parity operation, there are different situations or scenarios, each of which calls for a different subset of coefficients. For example, one scenario occurs when adding data segment x₅ to a stripe, when coefficients p₅ and q₅ are needed. Another scenario occurs when adding data segment x₆ to a stripe, when coefficients p₆ and q₆ are needed.

[0042] Coefficient Subsets

[0043]FIG. 3 shows a memory array 30 that contains plurality of coefficient subsets 31. Each coefficient subset is a list or concatenation of pre-selected and/or pre-computed coefficients that are applied to corresponding segments of data to produce a parity computation result. In accordance with the invention, a different subset of coefficients is pre-selected and stored for each different operation scenario. The subsets are then formatted and packed in a linear memory array for reference and direct use by parity operation logic. Because different scenarios call for different numbers of coefficients, the subsets are not of the same length or size.

[0044] Each coefficient is a single byte in the described embodiment of the invention. The term “packed” means that the subsets or strings of coefficients are concatenated in linear memory, preferably with no intervening unused spaces, to conserve storage space.

[0045] There is a one-to-one correspondence between a coefficient in a subset and a segment of data (either a data segment or a parity segment) when performing the parity operation. Each coefficient is applied only to its corresponding data segment or parity segment to produce the result of the operation.

[0046] One coefficient subset is included in the array for each possible parity computation case or scenario. Unique indexing formulas are used to locate the beginning of a subset in the array for each specific computational scenario. Generally, the subsets are arranged in pairs, corresponding to computations involving P and Q, respectively.

[0047] Referring to FIG. 3, memory array 30 includes a plurality of classification groups 32, 33, 34, 35, and 36, each of which contains the coefficient subsets 31 corresponding to a particular parity operation classification. Each subset in a classification group has coefficients for a specific scenario that occurs within the group's classification. With one exception, the coefficient subsets are the same size within any given classification group.

[0048] Within array 30, particular classification groups are located by computing a group offset from the beginning of the array to the beginning of the group. This group offset is the base index into the array for the group. To locate a specific coefficient subset within a classification group, a subset offset from the beginning of the group is added to the base index. This produces an index into the array that locates the beginning of the desired coefficient subset.

[0049] In accordance with one embodiment of the invention, the general parity operation classifications are defined as follows:

[0050] 1. Parity Generation Operations—Partial or full new stripe that has no pre-existing data or parity.

[0051] 2. Parity Regeneration Operations Resulting from Added Segments—Incremental growth of a stripe by incorporating new data segments into the two parity segments.

[0052] 3. Parity Regeneration Operations Resulting from Segment Modification—Modification of a data segment that is already incorporated in the two parity segments (read/modify/write).

[0053] 4. Single Data Segment Reconstruction—Reconstruction of a single data segment using one of the parity segments and the surviving data segments from the strip. Reconstruction from either P or Q parity segments is supported because in the case of two failed storage devices, one of the failed storage devices may hold P or Q.

[0054] 5. Double Data Segment Reconstruction—Reconstruction of two data segments of a stripe using the two parity segments P and Q, and the surviving data segments from the stripe.

[0055] Structure of Classification 1 Coefficient Subsets

[0056] The first classification group 32 of the array contains the coefficient subsets for parity generation operations. A parity generation operation generates new P and Q segments from new data segments x₀ through x_(N−1). There are only two coefficient subsets in this classification group. The subsets correspond respectively to the generation of parity segments P and Q:

[0057] P: {p₀, p₁, . . . p_(N−1)} and

[0058] Q: {q₀, q₁, . . . q_(N−1)}

[0059] Each of these subsets is the same length (N).

[0060] Structure of Classification 2 Coefficient Subsets

[0061] The second classification group 33 of the array contains the coefficient subsets for parity operations that add incrementally to a stripe. This type of operation updates P and Q segments in combination with any given contiguous range of new or added data segments xa through x_(b) (where b<N and a<=b). There are multiple different scenarios of these operations, corresponding to every possible range a through b of data segments within data segments 0 through N−1. Each scenario calls for a different subset of coefficients. For example, if the new or added data segments are x₃ and x₄, the required coefficient subset to calculate P is {p₃, p₄}. If the new or added data segments are x₂ through x₅, the required coefficient subset to calculate P is {p₂, p₃, p₄, p₅}. The total of possible ranges within data segments 0 through N−1 depends on the value of N.

[0062] Each coefficient subset of classification group 2 contains two initial parameters that indicate whether the subset applies to calculations of P or to calculations of Q. Each of these initial parameters is set to either “0” or “1”. A value of “1” for the first of these coefficients indicates that the calculation involves parity segment P. A value of “1” for the second of these coefficients indicates that the calculation involves parity segment Q. Only one of these two parameters should be set equal to “1” at any given time.

[0063] The remaining coefficients in a Classification 2 subset are the sub-range of coefficients that are used to regenerate P and Q from newly added data stripes. Thus, the classification group contains a plurality of coefficient subsets of the form:

[0064] P: {1, 0, p_(a), . . . p_(b)}and

[0065] Q: {0, 1, q_(a), . . . q_(b)}

[0066] Classification group 33 includes a plurality of subsets such as these, depending on N, corresponding to every range of a through b, within the larger range of 0 through N−1. The coefficient subsets in this section of the array have varying lengths or sizes, equal to b−a for each operation scenario.

[0067] Within this classification group, coefficient subsets are arranged and grouped by length. That is, the coefficient subsets containing the smallest number of coefficients are placed in the initial part of the classification group. The coefficient subsets containing the largest number of coefficients are placed at the end of the classification group. Within each of these groupings, the coefficient subsets are arranged in order according to the lower coefficient subscript of the range that is covered by the coefficient subset. Thus, the subsets having a=0 are positioned first, the subsets having a=1 next, and so on.

[0068] Structure of Classification 3 Coefficient Subsets

[0069] The coefficient subsets in the third classification group 34 are used to update P and Q when a single data segment is modified. This type of operation updates P and Q segments, given a modified data segment x_(a).

[0070] As with the Classification 2 group, the first two parameters of each Classification 3 subset indicate whether the coefficients of the group are applicable to P calculations or to Q calculations. Each of these coefficients is set to either “0” or “1”. A value of “1” for the first of these coefficients indicates that the subset coefficients apply to parity segment P. A value of “1” for the second of these coefficients indicates that the subset coefficients apply to involves parity segment Q.

[0071] Each subset contains a single remaining coefficient, corresponding to the data segment x_(a) that is being modified:

[0072] P: {1, 0, p_(a)} and

[0073] Q: {0, 1, q_(a)}

[0074] The third classification group 34 includes N pairs of such subsets, corresponding to all values of a from 0 through N−1. Note that these subsets correspond to a special case of the Classification 2 coefficient subsets, in which a=b, and can therefore be used when adding a single new data segment to a stripe.

[0075] Structure of Classification 4 Coefficient Subsets

[0076] The coefficient subsets in the fourth classification group 35 are used to reconstruct a single data segment x_(a) based on one of the parity segments and the surviving data segments. The coefficients correspond closely to the Classification 1 coefficients, except that they are transformed according to the mathematics (f( )) of the chosen error correction code to perform a reconstruction operation:

P: {f(p ₀ , p _(a)), f(p ₁ , p _(a)), . . . , f(p _(a)), . . . f(p _(N−1) , p _(a))}

Q: {f(q ₀ , q _(a)), f(q ₁ , q _(a)), . . . , f(q _(a)), . . . f(q _(N−1) , q _(a))}

[0077] More specifically:

P: (p, q _(b) +p _(b) q _(a))⁻¹((q _(b) p ₀ +p _(b) q ₀), (q ₀ p ₁ +p ₀ q ₁), . . . q _(b) P, . . . ,(q _(b) p _(k) +p _(b) q _(k)), (q _(b) p _(k−1) +p _(b) q _(k+1)), . . . p _(b) Q+ . . . +(q _(b) p _(N−1) +p _(b) q _(N−1)))

P: (p _(a) q _(b) +p _(b) q _(a))⁻¹((q _(a) p ₀ +p _(a) q ₀), (q _(a) p ₁ +p _(a) q ₁), . . . ,q _(a) P+ . . . +(q _(a) p _(k) +p _(a) q _(k)), (q _(a) p _(k−1) +p _(a) q _(k+1)), . . . , p _(a) Q, . . . , (q _(a) p _(N−1) +p _(a) q _(N−1)))

[0078] The fourth classification group includes N pairs of such subsets, corresponding to all values of a from 0 through N−1. Note that in each subset, the coefficient f(p_(a)) or f(q_(a)) corresponds to data segment x_(a).

[0079] Structure of Classification 5 Coefficient Subsets

[0080] The coefficient subsets in the fifth classification group 36 are used to reconstruct two data segments x_(a) and x_(b) based on the two parity segments and the surviving data segments. The coefficients correspond closely to the Classification 1 coefficients, except that they are transformed according to the mathematics (f( ) of the chosen error correction code to perform a reconstruction operation:

x _(a) : {f(p ₀ , q ₀ , p _(a) , p _(b) , q _(a) , q _(b),), f(p ₁ , q ₁ , p _(a) , p _(b) , q _(a) , q _(b)), . . . f(p _(a) , p _(b) , q _(a) , q _(b)), . . . , f(p _(k) , q _(k) , p _(a) , p _(b) , q _(a) , q _(b)), f(p _(k+1) , q _(k+1) , p _(a) , p _(b) , q _(a) , q _(b)), . . . f(p _(a) , p ₀ , q _(a) , q _(b)), . . . , f(p _(N−1) , q _(N−1) , p _(a) , p _(b) , q _(a) , q _(b),)}

x _(b) : {f(p ₀ , q ₀ , p _(a) , p _(b) , q _(a) , q _(b)), f(p ₁ , q ₁ , p _(a) , p _(b) , q _(a) , q _(b)), . . . f(p _(a) , p _(b) , q _(a) , q _(b)), . . . , f(p _(k) , q _(k) , p _(a) , p _(b) , q _(a) , q _(b)), f(p _(k+1) , q _(k+1) , p _(a) , p _(b) , q _(a) , q _(b)), . . . , f(p _(a) , p ₀ , q _(a), q_(b)), . . . , f(p _(N−1) , q _(N−1) , p _(a) , p _(b) , q _(a) , q _(b))}

[0081] The fifth section of the array includes (N*(N−1))/2 pairs of such subsets, corresponding every possible combination of a and b within the range of 0 to N−1. Note that in each subset, the coefficient f(p_(a), p_(b), q_(a), q_(b)) corresponds to data segment x_(a) or x_(b), depending on which data segment is being reconstructed.

[0082] One possible implementation of these equations is as follows:

x _(a): (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(b) , p ₀ +p _(b) , q ₀), (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(b) , p ₁ +p _(b) , q ₁), . . . , (p _(a) , q _(b) +p _(b) , q _(a))⁻¹ q _(b), . . . ,(p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q ₀ , p _(k) +p ₀ , q _(k)), (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q ₀ , p _(k+1) +p ₀ , q _(k+1)), . . . ,(p _(a) , q _(b) +p _(b) , q _(a))⁻¹ p _(b), . . . ,(p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q ₀ , p _(N0−1) +p ₀ q _(N−1))

x _(b): (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(b) , p ₀ +p _(b) , q ₀), (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(a) , p ₁ +p _(a) , q ₁), . . . , (p _(a) , q _(b) +p _(b) , q _(a))⁻¹q_(a), . . . ,(p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(a) , p _(k) +p _(a) , q _(k)), (p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(a) , p _(k+1) p _(a) , q _(k+1)), . . . , (p _(a) , q _(b) +p _(b) , q _(a))⁻¹ p _(a), . . . ,(p _(a) , q _(b) +p _(b) , q _(a))⁻¹(q _(a) , p _(N−1) +p _(a) , q _(N−1))

[0083] Coefficient Subset Usage

[0084]FIG. 4 illustrates a method of performing parity operations in accordance with the array storage scheme described above. A first step 100 comprises classifying different parity operations into classifications that include parity segment generation operations, parity segment regeneration operations, and data segment reconstruction operations. More specifically, an operation is classified as either a parity generation operation, a parity regeneration operation resulting from added segments, a parity regeneration operation resulting from segment modification, a single data segment reconstruction operation or a double data segment reconstruction operation. Each classification of parity operations includes a plurality of different classification scenarios, each of which involves a respective subset of parity coefficients.

[0085] A step 102 comprises pre-calculating individual parity coefficients and preselecting subsets of parity coefficients for use in the different parity operations and the different scenarios of parity operations. This step is performed in accordance with the description already given.

[0086] A step 104 comprises storing all of the pre-selected parity coefficient subsets in an indexed linear memory array, where they can be accessed by parity computation logic. This step includes pre-formatting the coefficient subsets so that they can be efficiently utilized by hardware-based parity operation logic. In particular, the individual coefficients of each subset are packed in adjacent bytes or storage units and ordered in a way that is particular to the hardware-based parity operation logic. As a result of this step, the memory array contains a single coefficient subset corresponding to each different computation scenario.

[0087] The individual coefficients and the subsets of coefficients are packed with no intervening data elements. The subsets of the array are grouped and ordered as already described, with the coefficient subsets grouped into classification groups by order of their classifications. Within the second classification group, the subsets have varying sizes. In addition, the subsets in the second classification group are sub-grouped by size, and ordered in ascending order according to their lowest-numbered coefficient.

[0088] During parity operations, parity operation logic accesses the memory array to obtain the appropriate coefficient subsets for use in the different scenarios of parity operations. Thus, a step 106 comprises determining which of the stored subsets of parity coefficients is needed for a particular parity operation. This step involves determining the classification of the parity operation and a group offset into the linear memory array, indicating the beginning of the classification group corresponding to that parity operation classification. A subset offset is then calculated into the group, to the location of the desired coefficient subset.

[0089] Step 106 is straightforward except with regard to the second classification group. As described in detail above, the second classification group contains coefficient subsets of varying lengths or sizes, making it difficult to determine the offset of a particular coefficient subset. However, the inventors have discovered that when the second classification group is arranged as described, having ordered subgroups of same-sized coefficient subsets, an offset to a particular subgroup can be calculated as a function of the size of the coefficient subsets of the sub-group and of N (the largest number of coefficients contained by any sub-group). Specifically, the offset to a particular sub-group i corresponding to subset size L_(i) is equal to

((L _(i)−1)(12N+L _(i)(3N−2L _(i)−5))/6)−3(N−1).

[0090] This formula assumes the presence in each subset of the prepended pair of constants (described above) corresponding to P and Q. L, however, equals b−a. Within the sub-group i, the offset of a particular coefficient subset is equal to a(L_(i)+2). Thus, the overall offset into the classification group, for a range of coefficients corresponding to x_(a) through x_(b), is

(((L _(i)−1)(12N+L _(i)(3N−2L _(i)−5))/6)−3(N−1))+a(L _(i)+2).

[0091] The size of the second classification group is given by the following equation:

((N−1)(12N+N(3N−2N−5))/6)−3(N−1).

[0092] After determining the appropriate offset into the memory array, a step 108 is performed of reading the determined parity coefficient subset from memory. Step 110 comprises performing the particular parity operation with the subset of parity coefficients read from memory.

[0093] Disk Controller Operation

[0094]FIG. 5 illustrates the most pertinent components of a disk controller 200 in accordance with the invention. The disk controller includes a microprocessor 201 and associated memory 202. In addition, the disk controller has a hard disk interface component 203 and a communications component 204. The hard disk interface component provides a means of access to the hard disks associated with and controlled by the disk controller. The communications component acts as an interface between a host computer and the hard disk controller.

[0095] In addition to these components, hard disk controller 200 includes hardware-based parity operation logic 205 in the form of an application-specific integrated circuit (ASIC). The term “hardware-based” is intended to mean that this logic component, as opposed to software-based logic, does not retrieve and execute instructions from program memory. Rather, the logic component has dedicated, interconnected logic elements that process signals and data. Although hardware-based logic such as this is less flexible than a microprocessor or other instruction-based processors, hardware-based logic is often much faster than instruction-based logic.

[0096] In general, the disk controller operates as follows. Microprocessor 201 handles communications with the host computer and coordinates all data transfers to and from the host controller. In addition, the microprocessor coordinates all actual disk transfers. However, data is buffered in memory 202 prior to writing to disk. Parity operations are performed on data in memory 202 under the control of microprocessor 201.

[0097] During initialization, microprocessor 201 constructs a coefficient subset table 212 in memory 202. Subsequently, when it is time for a parity operation, microprocessor 201 determines the classification and scenario of the parity operation. Once this information is determined, the microprocessor creates a script that indicates the locations in memory 202 of one or more data segments and parity segments that will be the object of the parity operation. The script indicates an offset into the coefficient subset table at which the proper coefficient subset will be found for the parity operation, and the number of coefficients that are contained in the coefficient subset. The script also indicates the location in memory at which the result of the requested calculation is to be placed. Each script stores information for a single parity operation and the memory structure for storing such scripts is referred to herein as a task description block (TDB). The TDB is stored in a particular location in memory 202 and a pointer to that location (e.g., a 64-bit address) is stored in a TDB queue 214 in memory 202.

[0098] When a script is placed in memory, the hardware logic is notified by the presence of the pointer to the TDB for the script in queue 214. The hardware logic responds by (a) retrieving the designated coefficients, data segments, and parity segments, (b) performing the appropriate parity operation based on the designated coefficients, and (c) returning the data and/or calculated parity segments to memory. The hardware logic may also optionally indicate to microprocessor 201 that the operation has been successfully completed (or alternatively that it could not be successfully completed).

[0099] The hardware logic is configured to perform the various different parity operations by summing products of coefficients and data/parity segments. The different operations actually vary only in the number and choice of coefficients, data segments, and parity segments. These variables are specified by the script. Thus, the operations lend themselves very conveniently to hardware-based calculations.

[0100] Other co-pending U.S. Applications describe technologies useful in conjunction with the invention, including U.S. Patent Application attorney docket no.10001489, entitled “Methods And Arrangements For Improved Strip-Based Processing, to inventors Barry J. Oldfield and Robert A. Rust; U.S. Patent Application attorney docket no. 10001493, entitled “Memory Manager for a Common Memory, to inventors Barry J. Oldfield and Robert A. Rust; and U.S. Patent Application attorney docket no. 10971442-1, entitled “Efficient parity Operations,” to inventors Barry J. Oldfield, Robert A. Rust and Michael B. Jacobson. These applications are hereby incorporated by reference.

[0101] Result Buffers

[0102] One of the goals of the presently described system is to generate or calculate the parity segments, in this case P and Q, as quickly and efficiently as possible. Recall that the parity segments are calculated from the data segments x₀ through x_(N−1), from a first set of parity coefficients p₀ through p_(N−1), and from a second set of parity coefficients q₀ through q_(N−1) in accordance with the following equation, which is discussed in detail above:

P=p ₀ x ₀ +p ₁ x ₁ +p ₂ x ₂ +p _(N−1) x _(N−1)

Q=q ₀ x ₀ +q ₁ x ₁ +q ₂ x ₂ +q _(N−1) x _(N−1).

[0103] One way of calculating P and Q is to read in, from external memory, one or more data segments, operate on the data segments to provide an intermediate computation result, and output the intermediate computation result to external memory. Next, the intermediate computation result is read in from external memory and processed with additional data segments (and coefficients) that are read in from external memory to provide a second intermediate computation result that is output to the external memory. Having to read from and write to external memory multiple times during creation of the parity segments is undesirably slow because of, among other reasons, the mechanics of, and overhead associated with performing the external memory read and write operations, as will be understood and appreciated by those of skill in the art.

[0104]FIG. 6 shows one implementation of a parity calculation module 600 that dramatically reduces the number of times external memory must be read from and written to during the calculation of the parity segments. This enables the parity segments to be calculated quickly and efficiently. The parity calculation module is advantageously implemented in hardware and, most preferably, comprises an ASIC. The exemplary module 600 includes an input buffer 601 and one or more result buffers. In this particular example, two exemplary result buffers 602, 604 are provided. Each result buffer is associated with an individual parity segment. Accordingly, in this example, result buffer 602 is associated with parity segment P, and result buffer 604 is associated with parity segment Q. In this example, the result buffers are implemented as SRAMs (Synchronous RAMs). It will be appreciated that multiple result buffers can be implemented by a single SRAM. For example, the two illustrated result buffers 602, 604 can be implemented by a single SRAM. Doing so, particularly where the parity calculation module 600 is implemented as an ASIC, carries with it advantages that include chip real estate savings, as will be appreciated by those of skill in the art.

[0105] Also included is one or more mathematical operator components. In the present example, two such mathematical operator components 606, 608 are provided and are each individually associated with a respective one of the result buffers 602, 604. Specifically, in this example, mathematical operator component 606 is coupled with result buffer 602 through an output line 606 a, and mathematical operator component 608 is coupled with result buffer 604 through an output line 608 a. The mathematical operator components are implemented, in this example, as finite math operators embodied in hardware. In addition, each of the mathematical operator components comprises an input for data segments (input 610), an input for coefficients (P coefficient input 612 a, and Q coefficient input 612 b respectively), and an input for feedback from the respective result buffer with which the mathematical operator component is associated (inputs 614 a, 614 b respectively).

[0106] Further, the parity calculation module 600 can advantageously include one or more additional local memory components that can be utilized to maintain locally, data that is used in the calculation of the parity segments. For example, in the present case, local memory components 616, 618 are provided and respectively contain the precalculated parity coefficients that are respectively utilized during parity segment calculations. The parity coefficients are desirably read into the local memory component(s) so that they can be used over and over again without having to read them in multiple times from external memory, e.g. external DRAM, which can be very slow. In addition, (although not specifically illustrated) a local memory component can be allocated for a task description block that can be read in from external memory. The task description block contains all of the addresses (or pointers) where the coefficients are located. As data segments are processed, address information that is maintained in the task description block can be locally updated and maintained for further use. This obviates the need to write any address information to external memory, which would necessarily slow the parity segment calculation down. Task description blocks and their use in the system described above are described in more detail in a co-pending U.S. Patent Application attorney docket no. 10001494, entitled “Using Task Description Blocks To Maintain Information Regarding Operations”, to inventors Barry J. Oldfield and Robert A. Rust, which is hereby incorporated by reference.

[0107] As an overview that illustrates how the parity calculation module 600 can be used to calculate parity segments, consider the following. In a RAID disk array the data blocks and parity blocks are written to disks, as shown in FIGS. 1 and 2. All data blocks and parity blocks are saved on unique disk drives so that a failure of one drive will not cause the loss of two blocks. The data blocks and parity blocks that are associated with them are commonly referred to as a “RAID Stripe”. The word “stripe” is used in the industry to refer to the data and parity blocks in the form that they are written to disk. Since the disk array has to keep track of the locations of all of the data and parity blocks in the system, it is common to have relatively large block sizes. For example, in some systems, the data and parity blocks are 64 Kbytes(KB) or 256 KB in size. This is an important point in the context of the discussion appearing below. The word “form” was used above because we will use the words “stripe” and “block” when referring to data in SDRAM. The term “stripe”, however, generally refers also to the collection of 64 KB/256 KB blocks.

[0108] The parity engine or calculation module in the described system is located in a custom ASIC that operates on data stored in Synchronous DRAM(SDRAM). Of course, other types of external memory, e.g. Dual Data Rate DRAM, can be used with SDRAM constituting but one exemplary type. When the calculations are complete, a separate operation takes place to write data and parity blocks to disk.

[0109] The parity logic does not read or write to disk, it always reads or writes to external memory(SDRAM). (Sometimes the data blocks are being written to disks while the parity calculation is being performed “in the background” to improve system performance. In these cases, the data blocks are still maintained in SDRAM until the parity calculations complete.)

[0110] Referring now to an exemplary parity calculation process—Assume 64 KB data blocks A, B, C, D are being processed to produce parity blocks P & Q for this example.

[0111] Data blocks A, B, C, & D are placed in memory external to the ASIC—in this case SDRAM. This external memory is much larger than is practicable to include internal to the ASIC.

[0112] A TDB (described in detail in the application incorporated by reference above) is generated in SDRAM that has the following information:

[0113] Information about the type of calculation being performed

[0114] Pointers to the starting address locations of all data blocks. For data blocks A,B,C,D, the pointers will be referred to as Aa,Ba,Ca,Da where the lower case “a” stands for address

[0115] parity block starting address locations Pa & Qa

[0116] A length/size value for how big the data blocks are that are to be processed

[0117] Coefficient pointer to the starting address for the coefficients to be used

[0118] The queue number where the result message should be written after the calculation process completes.

[0119] A request is made to Background Task Logic (BGT) to perform the computations by writing an entry to a BGT request queue. The BGT performs tasks that are described by the TDBs. The request has information about what the operation is and a pointer to the TDB.

[0120] The BGT logic reads the request queue entry and reads in the TDB referenced by the request pointer. The TDB is saved in an internal memory inside the ASIC. In the illustrated and described implementation, the internal memory comprises an SRAM, but other types of internal memories are possible.

[0121] The BGT logic compares some field from the request queue entry with fields in the TDB to verify that the TDB is the one expected.

[0122] The BGT logic reads in the parity coefficients and stores them in an internal RAM.

[0123] The BGT logic now reads in part of the first data block and stores it in a temporary input buffer. In the FIG. 6 example, this constitutes input buffer 601. Only part of the first data block is read in because, in the described embodiment, the entire 64 KB block cannot be read in. It will be appreciated that in the future this may change. In the present, however, it is just not feasible to have multiple embedded 64 KB internal RAMs. In one current implementation of the logic, the internal buffers are sized at 512 bytes(1 KB=1024 bytes so a 512 byte buffer=½ KB). This is where a so-called “strip” comes into play. To avoid having to save many, many intermediate 512 byte buffers of data, a stripe is processed in 512 byte strips. Using 512 byte buffers, the data blocks are broken into 64 KB/0.5 KB=128 segments. The terminology A1-A128 will be used in the following discussion to describe the 128 segments that make up the 64 KB data block referred to as A. Continuing with the computation process. part of data block A is read in. To determine which part to read in, we first check the length value to make sure how much more data needs to be processed. If length>512 then, we use the Aa address pointer for the starting location and read in 512 bytes. This data is processed and a new value is saved into the TDB address pointer for A. (New Aa=Aa+512) Note that the TDB is stored in an internal RAM so the pointer updates cause no external memory accesses. P & Q buffers now contain intermediate data for the Al portion of the A1,B1,C1,D1 strip of the stripe. If length<512 then, we use the Aa address pointer for the starting location and read in “length” bytes. This data is processed and a new value is saved into the TDB address pointer for A=(New Aa=Aa+length). P & Q buffers now contain intermediate data for the A1 portion of the A1,B1,C1,D1 strip of the stripe.

[0124] This process is repeated for the remaining block segments (i.e. B, C, & D for this example).

[0125] P & Q segments are then written out to SDRAM at locations Pa & Qa, and the Pa & Qa pointers are updated in the same manner as data block pointers were updated.

[0126] Now the length value is updated. If length>512, New length=length-512. Since length is a positive number, we still have strips to process. The above-described process is repeated from the point where the BGT logic reads in part of the first data block and stores it in temporary input buffer 601 until the length value is less than or equal to 512.

[0127] If the length value is less than or equal to 512, length=0 and processing for the whole stripe has completed. For this example the process of reading in part of the first data block, storing it in a temporary input buffer and processing it as described above will have been executed 128 times. The first time through will process A1,B1,C1,D1 and write out P1&Q1. The last time through, A128, B128, C128, D128 will be processed and P128 & Q128 will be written.

[0128] It will be appreciated and understood that the above described process can perform calculations on any depth of data blocks. The length value can be anything from 8 bytes in size to many megabytes (MB). One restriction with the specific approach described above is that the length must be an integer number of 8 byte words since we perform our calculation 8 bytes at a time. In the generic case, the width of processing is unimportant.

[0129] Subsequently, the process writes a completion indication to the result queue that was listed in the TDB. The result entry will contain status bits that indicate if the process was successfully completed or if it had errors. The process can now be repeated for additional parity segments.

[0130]FIG. 7 is a flow diagram that describes an exemplary method in accordance with the described embodiment. The presently described method can be implemented in connection with the parity calculation module 600 of FIG. 6.

[0131] Step 700 receives one or more data segments. In the illustrated example of FIG. 6, a data segment is received by each of the mathematical operator components 606, 608. Step 702 receives one or more parity coefficients. In this example, parity coefficients are received by each of the mathematical operator components 606, 608. Advantageously, the parity coefficients can be locally maintained in local memory components (such as components 616, 618) so that the system need not access external memory multiple times.

[0132] Assuming that, at this point in the processing, this is the first pass through the mathematical operator components 606, 608 for purposes of calculating one or more parity segments, step 704 operates on at least one data segment and on at least one parity coefficient to provide an intermediate computation result. In the present example, each of the mathematical operator components 606, 608 can operate on one or more of the data segments and each segment's associated coefficient in order to provide the intermediate computation result. On the first pass through the mathematical operator components, feedback that is provided by the result buffers via lines 614 a, 614 b does not affect the computations that are performed by the mathematical operator components. This can be done a number of ways. For example, any feedback that is provided on the first pass can simply be ignored by the mathematical operator components. The feedback can also simply be zeroed out on the first pass through. Additionally, although less efficient, the relevant contents of the SRAM can simply be zeroed out for the first pass through. This is less desirable because it takes more time and processing overhead.

[0133] Having operated on the data segment(s) and parity coefficient(s) to provide the intermediate computation result, step 706 then writes the intermediate computation result to one or more local result buffers. In the presently-described example, the result buffer comprises an SRAM. In the FIG. 6 implementation, there are two separate SRAMs—one for each parity segment. Using an SRAM to implement the result buffer(s) is advantageous in that operations can take place on each edge of a clock in the clock cycle. This will become more apparent below.

[0134] After the intermediate computation result is written to the result buffer, step 708 receives one or more data segments, one or more parity coefficients, and at least one intermediate computation result from the result buffer. This step is implemented, in this example, by each of the mathematical operator components 606, 608. Specifically, the components receive the data segment(s) and coefficient(s) as described above. Additionally, however, the mathematical operator components 606, 608 also receive, via feedback inputs 614 a, 614 b, the respective intermediate computation results that were previously written to the result buffers. The mathematical operator components 606, 608 then operate, at step 710, on the data segment(s), coefficient(s), and the intermediate computation results to either provide an additional intermediate computation result, or a calculated parity segment. If another intermediate computation result is provided, steps 706-710 are repeated until the parity segment is calculated.

[0135] Use of one or more SRAMs to implement multiple local result buffers is advantageous in that multiple operations can be performed within one clock cycle. Specifically, within every clock cycle, intermediate computation results can be retrieved from the result buffers, operated upon by the mathematical operator components, and written back into the result buffers for the next clock cycle. This approach is extremely fast and greatly improves upon techniques that utilize multiple accesses to external memory as described above.

CONCLUSION

[0136] The parity calculation architecture described above has a number of advantages over the prior art. One significant advantage is that the architecture allows parity computations to be performed by hardware-based logic, without requiring significant complexity in the hardware. To provide this advantage, a microprocessor performs preliminary work such as designating the various parameters to be used in the calculations. Once the proper coefficients and data/parity segments have been designated, the hardware can perform the actual calculations in similar or identical ways, regardless of the particular type of operation that is requested.

[0137] The pre-selection of coefficient subsets, and their arrangement in memory, provides further efficiencies by eliminating many steps that would otherwise be required to select coefficients prior to every parity operation. Furthermore, the unique indexing method, particular with regard to the described second section of the array, allows the coefficients to be packed in memory to save space, even though the coefficient subsets have differing lengths.

[0138] Although the invention has been described in language specific to structural features and/or methodological steps, it is to be understood that the invention defined in the appended claims is not necessarily limited to the specific features or steps described. Rather, the specific features and steps are disclosed as preferred forms of implementing the claimed invention. 

1. A method of calculating parity segments comprising: providing a parity calculation module configured to calculate one or more parity segments, the parity calculation module being embodied as an application-specific integrated circuit (ASIC); with the ASIC: receiving one or more data segments that are to be used to calculate one or more parity segments; receiving one or more parity coefficients that are to be used to calculate the one or more parity segments; operating on the one or more data segments and the one or more parity coefficients to provide an intermediate computation result; writing the intermediate computation result to one or more local buffers on the ASIC; and using the intermediate computation result from the one or more local buffers to calculate one or more parity segments.
 2. The method of claim 1, wherein the ASIC has multiple local memory components to hold data that is used in the calculation of the parity segments.
 3. The method of claim 1, wherein said act of operating is performed by one or more finite mathematical operator components.
 4. The method of claim 1 further comprising maintaining multiple parity coefficients in one or more local memory components on the ASIC thereby reducing external memory access operations.
 5. The method of claim 4, wherein said receiving one or more parity coefficients comprises receiving the coefficients from the one or more local memory components and into one or more finite mathematical operator components that are configured to provide the intermediate computation result.
 6. The method of claim 1 further comprising providing feedback from the one or more local buffers to one or more mathematical operator components that are configured to perform said operating.
 7. The method of claim 6 further comprising: receiving one or more additional data segments that are to be used to calculate one or more parity segments; receiving one or more additional parity coefficients that are to be used to calculate the one or more parity segments; receiving the intermediate computation result from the one or more local buffers; operating on the one or more additional data segments, the one or more additional parity coefficients, and the intermediate computation result to provide a result; and writing the result to one or more local buffers on the ASIC.
 8. The method of claim 7, wherein said result that is provided by said operating on the one or more additional data segments, the one or more additional parity coefficients, and the intermediate computation result comprises an additional intermediate computation result.
 9. The method of claim 7, wherein said result that is provided by said operating on the one or more additional data segments, the one or more additional parity coefficients, and the intermediate computation result comprises one or more parity segments.
 10. The method of claim 7, wherein said one or more local buffers comprise SRAMs.
 11. The method of claim 7, wherein said one or more local buffers comprise SRAMs, and said acts of claim 7 are performed within one clock cycle of a system clock.
 12. The method of claim 6 further comprising not affecting computations performed by the one or more mathematical operator components with said feedback on a first pass through the one or more mathematical operator components.
 13. The method of claim 12, wherein said not affecting comprises zeroing out the feedback.
 14. The method of claim 1, wherein said one or more local buffers comprise SRAMs.
 15. A method of calculating parity segments comprising: providing a parity calculation module configured to calculate one or more parity segments; with the parity calculation module: receiving one or more data segments that are to be used to calculate one or more parity segments; receiving one or more parity coefficients that are to be used to calculate the one or more parity segments; operating on the one or more data segments and the one or more parity coefficients to provide an intermediate computation result; writing the intermediate computation result to one or more local buffers; and within one clock cycle of an associated clock, receiving (a) the intermediate computation result from the one or more local buffers, (b) one or more additional data segments and (c) one or more additional parity coefficients, and operating on them to provide a result that is stored in the one or more local buffers.
 16. The method of claim 15, wherein the parity calculation module comprises an application specific integrated circuit (ASIC).
 17. The method of claim 15, wherein the one or more local buffers comprise SRAMs.
 18. The method of claim 15, wherein the parity calculation module comprises an application specific integrated circuit (ASIC), and the one or more local buffers comprise SRAMs on the ASIC.
 19. The method of claim 15, wherein the parity calculation module comprises one or more local memory components configured to locally hold data that is used in the calculation of the parity segments.
 20. The method of claim 19, wherein the one or more local memory components hold parity coefficients.
 21. The method of claim 20, wherein the one or more local memory components hold a task description block which is used to access the parity coefficients.
 22. The method of claim 21 further comprising updating address information that is contained in the task description block that is held in the one or more local memory components.
 23. A parity segment calculation module comprising: an application specific integrated circuit (ASIC) having at least: one or more result buffers for holding intermediate computation results; one or more mathematical operator components configured to receive data segments and coefficients associated with the data segments and operate on them to provide intermediate computation results that can be written to the one or more result buffers; and one or more feedback lines, individual lines being coupled between an associated result buffer and an associated mathematical operator component, to provide an intermediate computation result to the math operator for use in calculating parity segments.
 24. The parity segment calculation module of claim 23, wherein the one or more result buffers comprise at least one SRAM.
 25. The parity segment calculation module of claim 23, wherein the one or more result buffers comprise multiple SRAMs.
 26. The parity segment calculation module of claim 23, wherein the one or more result buffers comprise two SRAMs.
 27. The parity segment calculation module of claim 23 further comprising one or more memory components configured to hold the coefficients locally on the ASIC.
 28. The parity segment calculation module of claim 27, wherein the one or more memory components hold at least one task description block that is utilized to access the coefficients. 